Practicing Success

Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Algebra

Question:

What is the value of $ ( a+ b+ 2c) (a^2 + b^2 +4c^2 - ab - 2bc -2ca )$?

Options:

$ a^3 - b^3 - c^3 - 6abc $

$ a^3 + b^3 + 4c^3 - 6abc $

$ a^3 - b^3 - 8c^3 - 3abc $

$ a^3 + b^3 + 8c^3 - 6abc $

Correct Answer:

$ a^3 + b^3 + 8c^3 - 6abc $

Explanation:

What is the value of $ ( a+ b+ 2c) (a^2 + b^2 +4c^2 - ab - 2bc -2ca )$

Put the value of a , b and c =1 and satisfy from the equation

$ ( a+ b+ 2c) (a^2 + b^2 +4c^2 - ab - 2bc -2ca )$ = $ ( 1+ 1+ 2) (1 + 1 +4 ×1 - 1 - 2×1 -2×1 ) = 4 ( 6 - 5 ) = 4

If we take option 4 = $ a^3 + b^3 + 8c^3 - 6abc $

Put the values in this equation  = $ 1 + 1 + 8 ×1 - 6 $ = 4 satisfied